Accessing Visual Voicemail and receiving notifications of new voicemails is not working now that I upgraded to iOS 7, using carrier T-Mobile, am I alone?

Try a Restart.

Press and hold the Sleep/Wake button for a few seconds until the red "slide to power off" slider appears, and then slide the slider. Press and hold the Sleep/Wake button until the Apple logo appears.

Resetting your settings

You can also try resetting all settings. Settings>General>Reset>Reset All Settings. You will have to enter all of your device settings again.... All of the settings in the settings app will have to be re-entered. You won't lose any data, but it takes time to enter all of the settings again.

Resetting your device

Press and hold the Sleep/Wake button and the Home button together for at least ten seconds, until the Apple logo appears. Apple recommends this only if you are unable to restart it.

Or if this doesn't work and nobody else on the blog doesn't have a better idea you can contact Apple.

Here is a link to their contacts with most of the information below.

http://www.apple.com/contact/

I have the exact same issue. Tried calling T-Mobile several times to no avail. Followed all the instructions from various threads including: Phone restore, reset network settings, reset voicemail password, power phone off and on, hard reset, etc... still no answers and it's still not working.

This doesn't sound like your issue at all, but if you turn off cellular in your settings and are doing wi-fi calling only, your visual voice mail will not be available until you turn cellular back on.

I was able to fix the issue only after visiting my local T-Mobile store and getting a new SIM card. Once they put it in, it worked right away.